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DeLLMa: Decision Making Under Uncertainty with Large Language Models
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Proposes DeLLMa, a multi-step inference-time framework that combines LLM state enumeration, state forecasting, Bradley-Terry utility elicitation, and expected-utility maximization to improve LLM decisions under uncertainty.
Problem
LLMs prompted directly (zero-shot, self-consistency, chain-of-thought) make poor decisions under uncertainty, especially as the number of actions grows; decisions also need to be human-auditable.
Approach
Scaffold LLM reasoning on classical decision theory: enumerate latent states, forecast verbalized probabilities for them, elicit a utility function from LLM pairwise rankings of sampled state-action pairs via Bradley-Terry, then pick the action with maximum Monte Carlo expected utility, with batching and variance reduction for utility elicitation.
Key results
- DeLLMa variants give up to a 40% increase in decision accuracy over competing prompting methods on Agriculture, and improve accuracy across GPT-4, Claude 3, and Gemini 1.5.
- With 64 samples per action, DeLLMa reaches 73.3% accuracy on Agriculture and 64.2% on Stocks, versus 33.3% and 35.0% for o1-preview.
- LLM-human preference agreement for utility elicitation is 70.4% (GPT-4), 65.3% (Claude 3), and 69.6% (Gemini 1.5), comparable to 77.5% inter-annotator agreement.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use DeLLMa instead of zero-shot prompting | LLM decision making · Agriculture and Stock | accuracy | Helped |
| use DeLLMa instead of o1-preview | LLM decision making · Agriculture | accuracy: 73.3% vs 33.3% | Helped |
| use DeLLMa instead of o1-preview | LLM decision making · Stock | accuracy: 64.2% vs 35.0% | Helped |
| replace the forecast distribution with a uniform distribution (ablation) | DeLLMa · Agriculture accuracy with GPT-4 and Gemini 1.5 | accuracy: GPT-4: 60.0% -> 58.3%; Gemini 1.5: 47.5% -> 45.8% | No clear effect |
| remove a randomly selected latent factor (ablation) | DeLLMa · Agriculture accuracy with GPT-4 and Gemini 1.5 | accuracy: GPT-4: 60.0% -> 55.0%; Gemini 1.5: 47.5% -> 42.5% | No clear effect |
| add unrepresentative or redundant latent factors (ablation) | DeLLMa · Agriculture accuracy with GPT-4 and Gemini 1.5 | accuracy: GPT-4: 60.0% -> 56.7%; Gemini 1.5: 47.5% -> 45.8% | No clear effect |
| replace the forecast distribution with a uniform distribution (ablation) | DeLLMa · Agriculture accuracy with Claude 3 | accuracy: 40.8% -> 32.5% | Hurt |
| remove a randomly selected latent factor (ablation) | DeLLMa · Agriculture accuracy with Claude 3 | accuracy: 40.8% -> 34.2% | Hurt |
| add unrepresentative or redundant latent factors (ablation) | DeLLMa · Agriculture accuracy with Claude 3 | accuracy: 40.8% -> 35.8% | Hurt |
| increase inference-time sample size (ablation) | DeLLMa · Agriculture | accuracy | Helped |
| increase minibatch overlap percentage (ablation) | DeLLMa · Agriculture | accuracy | Helped |
| use full pairwise rankings instead of one-vs-all comparisons (ablation) | DeLLMa utility elicitation · Agriculture | accuracy | Helped |
Surprising findings
- On larger action sets, zero-shot, self-consistency and CoT baselines often underperform random guessing on Agriculture, as they echo context sentiment.
- On Stocks, DeLLMa-Top1 outperforms DeLLMa-Pairs, which the authors attribute to LLM hallucination in full rankings of volatile data.
Limitations
- Limited to small discrete state and action spaces due to context window size.
- Not tested on sequential decision making or portfolio (weighted combination) decisions.
- Deploying without guardrails could cause financial losses; LLM hallucination in rankings can add noise.
Experimental setup
Datasets: USDA Fruits & Nuts report (September 2021) USDA California price and yield statistics Yahoo Finance monthly stock prices (Dec 2021 to Nov 2023)
Benchmarks: Agriculture decision problems (120 instances) Stocks decision problems (120 instances)
Metrics: decision accuracy normalized utility ECE NLL agreement with human preference
Baselines: Zero-Shot Self-Consistency Chain-of-Thought OpenAI o1-preview DeLLMa (Naive)
Builds on: chain-of-thought self-consistency tree-of-thoughts Bradley-Terry model
Closest papers by meaning
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